Microcantilever chemical and biological sensors operate by undergoing specific changes upon interactions with analytes. One great advantage of the cantilever technique is that five response parameters (resonance frequency, phase, amplitude, Q-factor, and deflection) can be simultaneously detected. The resonance frequency, f, of an oscillating microcantilever can be expressed as:
                    f        =                              1                          2              ⁢              π                                ⁢                                    k                              m                *                                                                        (        1        )            where k is the spring constant of the lever and m* is the effective mass of the microcantilever. The effective mass can be related to the mass of the beam, mb, through the relation m*=nmb, where n is a geometric parameter. Typical values for n are 0.14 for a v-shaped cantilever and 0.24 for a rectangular cantilever. Both changes in the effective mass and changes in the spring constant can affect the resonance frequency.
The spring constant can also change due to adsorption processes in which a substance is taken upon the surface of a cantilever which changes the mass and surface stress of the cantilever, resulting in a change in resonance of the cantilever. To account for this, Eq. (1) can be modified as:
                              f          2                =                              1                          2              ⁢              π                                ⁢                                                                      k                  +                                      δ                    ⁢                                                                                  ⁢                    K                                                  ⁢                                                                                                                m                  *                                +                                  nδ                  ⁢                                                                          ⁢                  m                                                                                        (        2        )            where the initial resonance frequency f1, changes to f2 due to adsorption. In this equation, k changes to k+δk as a result of adsorption induced surface stress while m* changes to m*+nδm due to mass loading. Surface stress on the top and bottom of the cantilever (denoted by s1, and s2) are balanced at equilibrium. Upon differential adsorption on the two surfaces, they can become unequal and cause bending of the cantilever. The change in the spring constant due to surface stress is given by:
                              δ          ⁢                                          ⁢          k                =                                                            π                2                            ⁢              n                                      4              ⁢                              n                1                                              ⁢                      (                                          δ                ⁢                                                                  ⁢                                  s                  1                                            +                              δ                ⁢                                                                  ⁢                                  s                  2                                                      )                                              (        3        )            where n1 is a geometric factor for v-shape cantilevers, and δs1=(s1−s′2) and δs2=(s2−s′2) are changes in surface stress on the top and the bottom surface of the cantilever before and after adsorption. Adsorption induced changes in the surface stress on one side of the microcantilever results in measurable bending or static deflection of the microcantilever, which can be employed as a transduction or sensing mechanism. A sensing microcantilever can be created by applying a thin chemoselective coating to one side of the cantilever to take up a selected chemical compound and produce the change in cantilever resonance.
Static bending can be pronounced and measurable, however, in most cases, changes in k and m due to adsorption are small. The resonance frequency after adsorption can be approximated by Eq. (4)
                              f          2                =                              f            1                    ⁡                      [                          1              +                                                1                  2                                ⁢                                  (                                                                                    δ                        ⁢                                                                                                  ⁢                        k                                            k                                        -                                                                  δ                        ⁢                                                                                                  ⁢                                                  m                          *                                                                                            m                        *                                                                              )                                                      ]                                              (        4        )            and is valid as long as δm<<mb and δk<<k:
Thermally induced oscillations have been exploited to study cantilever properties including the spring constant and Q. This method takes advantage of the equipartition theorem applied to cantilever potential energy:
                              〈                                    1              2                        ⁢                          mf              o                        ⁢                          x              2                                〉                =                              1            2                    ⁢                      k            B                    ⁢          T                                    (        5        )            where fo is the resonant frequency, kB is Boltzman's constant, m is the mass, T the absolute temperature, and x2 is the mean squared cantilever displacement in any one mode. The mean squared displacement is available from an integral under the square of the power spectral curve. The spring constant is obtained by:k=kBT/<x2>   (6)Thermal resonance frequency and the spring constant can be obtained as mentioned above by acquiring the power spectrum for the resonance using the frequency modulation method.
For a sensor that depends on vapor sorption processes, the chemical interface between the transducer and ambient air is a vital aspect in its successful operation. It is standard procedure to coat microcantilevers on one side to enhance sensitivity and induce chemical selectivity through the choice of coating material. For example in the case of hazardous vapor sensors, microcantilevers have been coated with 1–10 nm of a chemoselective polymer. These are usually polymers that readily experience sorption in the presence of the analyte and undergo changes such as inhomogeneous swelling as the molecules are adsorbed. Swelling results in deflection of the cantilever and a change in its resonance frequency. The cantilever/coating system acts as a molecular recognition system in which the sensing function is manifested as a change in the cantilever's state and/or properties. Similarly, sensors for biomolecules are easily functionalized on the gold side of a gold-coated microcantilever via dipping the cantilevers in solutions containing tethering molecules such as thiol-groups. Depending on the choice of receptor molecule, the cantilever can be used to detect specific proteins, DNA segments, and other biomolecules.
Many polymer-toxic vapor systems that are useful for sensor applications have been identified by researchers. These materials have been identified by examining the response of a coated surface acoustic wave sensor exposed to a particular analyte. The response depends on a partitioning phenomena in which the partition coefficient, B, represents the equilibrium vapor-polymer solubility at a given temperature. The partition coefficient measures the overall strength of interaction and is equal to Cp/Cv where Cv is the vapor concentration in the gas phase, while Cp is the concentration in the polymer. Larger values of B indicate stronger interactions. The values of B for various polymer-toxic vapor systems can be obtained through gas-liquid chromatographic (GLC) analysis.
Chemoselective polymers have been tailored for enhanced sorption of molecular species by increasing the active surface area as well as by considering coating-vapor solubility interactions. Specifically, polymer-vapor systems that experience weaker, reversible interactions at ambient temperatures (e.g. hydrogen bonding, dispersion, and dipole-dipole interactions) have been optimized while systems that tend to form strong irreversible covalent bonds have been avoided. A class of polymer coatings and corresponding molecular sorbents have been developed that undergo spontaneous regeneration at room temperature after the vapor is removed from the ambient.
Various methods are employed to coat cantilevers including the use of nanoinjectors, microspray methods, and functionalization by dipping the cantilevers in a reagent to produced adsorbed layers such as self-assembled monolayers (SAMs). The choice of the process of coating microcantilevers is dependent upon the nature of the coating being employed. Moreover, in the case of microcantilever arrays a coating method is required that permits individual microcantilevers to have a unique coating compared to the other microcantilevers in the array.
In one deposition method, self-assembled monolayers (SAMs) of molecules such as alkanethiols are formed on the gold-coated side of microcantilevers to detect a wide variety of analytes in both liquid and vapor environments. SAMs have been developed for different sensing applications including metal ions in water and vapors of explosive chemicals such as trinitrotoluene (TNT) and cyclotrimethylenetrinitramine (RDX). Since SAMs are deposited by dipping cantilevers in a reagent, an approach is needed to coat unique SAMs on individual microcantilevers in an array. This deposition technique has been demonstrated using micro-capillaries, and the resultant functionalized microcantilever array was used for label-free detection of two cardiac biomarker proteins. SAMs represent one path toward the functionalization of individual microcantilevers in an array as long as the requisite microfluidic functionalization apparatus is developed for a particular cantilever array.
An alternative deposition technique that may be employed to selectively coat cantilevers with specific polymer sensing layers is matrix assisted pulsed laser evaporation (MAPLE). This technique involves dispersal of the target material in an organic host followed by evaporation in vacuum with a pulsed laser. This method is a generic process that has successfully deposited thin films of a wide range of chemoselective materials, including highly adsorptive chemoselective polymers. MAPLE permits precise control over polymer deposition thickness with a high degree of uniformity, and retains all the original physicochemical properties of the chemoselective polymer. Also, MAPLE allows for localized coating deposition using non-contact shadow masking with micron-sized features that meet the required dimensions of the cantilever technology. Arrayed cantilever sensors can be coated with different polymers employing multiple targets in the MAPLE deposition chamber and a moveable shadow mask. In a manufacturing process many sensor array chips can be simultaneously coated with a high degree of control.
Bending and resonance frequency shifts of a cantilever are typically measured using techniques perfected for atomic force microscopy. These include optical reflection, piezoresistive, capacitive, and piezoelectric methods. However, these methods are not easily adapted for detection of cantilever motion in microcantilever sensor arrays. For example, the laser-beam reflection technique is quite sensitive but does not scale well as the number of microcantilevers in an array becomes large. The piezoresistive method has less measurement sensitivity but is amenable to standard microprocessing techniques for large number of cantilevers. However, the piezoresistive method cannot be easily adapted to liquid ambients. The capacitive method measures changes in capacitance between the cantilever and an adjacent surface, yet this close proximity causes complications due to electrostatic interactions that lead to stiction, among other issues. Therefore there is a need in the art for development of microcantilever sensors that may be amenable to miniaturization and scalable to an array of microcantilevers on a single chip. Additionally, there is also a need in the art for a microcantilever sensor that is suitable in both vapor and liquid environments, and therefore new methods of detecting microcantilever motion must be developed.